# (Solved Homework): Parametric Graph is shown below x = sin t + sin 1.5t, y = cos t Consider the equation x = sin t + sin 1.5t, r = cos t Differentiate With respect to 't'…

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Parametric Graph is shown below x = sin t + sin 1.5t, y = cos t Consider the equation x = sin t + sin 1.5t, r = cos t Differentiate With respect to ‘t’

For 2 functions to be graphed simpultaneously, we have to use ParametricPlot[{fx,fy},{t,tmin,tmax}]

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(Solved Homework): Parametric Graph is shown below x = sin t + sin 1.5t, y = cos t Consider the equation x = sin t + sin 1.5t, r = cos t Differentiate With respect to 't'…
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Here fx is function of x and fy is function of y.

Consider fx=sin1.5t+sint

sin has a periodicty of 2$\fn_cm \pi$ So fx will be periodic when sin 1.5t as well as sin t are same as sin 2$\fn_cm \pi$. Or when 1.5t and t are multiples of 2$\fn_cm \pi$. This happens at t=4$\fn_cm \pi$. Hance fx has periodicity of 4$\fn_cm \pi$

Now consider fy=cost. This has periodicity of 2$\fn_cm \pi$.

So conidering periodicty of both fx and fy, the periodicty for the common graph will be 4$\fn_cm \pi$. So lets take tmin as 0 and tmax as 4$\fn_cm \pi$.

Hence we can use the following statement:

ParametricPlot[{sin[t]+ sin[1.5t], cos t},{t,0,4 pi}]

Output:

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